Mayor Thomas M. Menino defended his decision Friday to keep schools open as a late winter storm surprised Boston with more than a foot of snow.

Almost 40 percent of the city’s 57,000 public school students stayed home, leaving empty desks and vacant seats on the city’s fleet of 700 buses. Forecasts varied drastically and all underestimated the amount and duration of the snow, which city officials had expected to peter out by 9 a.m.

The storm roared well into the afternoon, burying Hyde Park, Roslindale, and the western reaches of Boston with well over a foot snow. By 1 p.m., almost 13 inches had fallen at Logan International Airport. The morning commute was particularly difficult, with some school buses in Boston running as much as an hour late. Buses fared much better on the trip home in the afternoon.

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“Everyone is saying, ‘Why didn’t you cancel school?’ ” Menino asked in a telephone interview. “What about that family who has to go to work? What are they going to do with their child? Have them sit in front of a TV all day? I’d rather have them in school.”

Students who stayed home Friday will not be penalized or marked absent. Scores of smaller school districts did cancel classes, including Newton, Hull, Mansfield, and Newburyport. Other large school districts kept school districts open, including Somerville, Brookline, and Cambridge, where Superintendent Jeffrey Young checked conditions at 4:15 a.m.

“The streets were clear, pavement visible,” said Young, who gave the go-ahead for classes. “This is a call you have to make by 5 a.m.”

Brookline Superintendent William H. Lupini sounded a similar note. “If I had the information I had at 11 a.m. at 5 a.m., I would’ve made a decision to close,” Lupini said. “A lot of parents complained, but you work the best you can with the information you have, erring on the side of keeping your students, family, and staff safe.”

At 4 a.m., the National Weather Service issued a forecast that predicted 6 to 8 inches of snow in Boston. City officials often decide the night before a storm whether classes will be canceled. Administrators try to give parents advance notice so they can make daycare arrangements. The city also coordinates with community centers, which typically open as a resource for parents.

Bus drivers reported to work an hour early Friday, which meant they arrived at 4 a.m. or 4:30 a.m. to clean snow off their vehicles and perform regular safety checks, according to Lee McGuire, spokesman for Boston Public Schools. At that hour, the city’s bus yards had been cleared to the pavement and trucks had been salting and plowing outside schools.

Buses start heading out at 5 a.m., and the first child is typically picked up around 6 a.m., McGuire said. If classes are to be canceled, the call must be made before buses pull out of the yard and children climb aboard.

“We got conflicting forecasts during the night and morning about how much snow and when it was going to [stop],” Menino said. “Calling school off at 5 or 6 in the morning doesn’t work. It doesn’t work for our schools and it doesn’t work for working parents.”

In a separate interview, City Councilor John R. Connolly said Menino should have “erred on the side of caution” and kept children at home.

“Predicting the weather is really hard, but if you were up at 5 a.m. this morning, you should have known that school should have been canceled,” said Connolly, who is running for mayor and will challenge Menino if he seeks another term this fall. “We have to put the safety of our children, teachers, and school staff first, and I don’t think we did that today.”

The school department did cancel after-school activities on short notice Friday afternoon, prompting many parents to venture through the snow to retrieve their children.

Outside the Tobin K-8 School on Mission Hill, Anet Garcia trudged through a snowbank, eager to bring home her second-grader before afternoon buses snarled traffic.

“Something like this, they should have canceled,” said Garcia, 46, of Jamaica Plain. “I mean, one more day at the end of the school year, it doesn’t matter.”

Standing nearby in the swirling snow, Marie Herivaux, 40, said it would have been safer for the city to cancel school. Herivaux’s car was stuck at home in Roxbury, so she walked about 20 minutes to pick up her sons, 13 and 7.